Measuring and
Constructing Segments
Why learn this?
You can measure a segment to calculate the
distance between two locations. Maps of a
race are used to show the distance between
stations on the course. (See Example 4.)

A ruler can be used to measure the distance between
two points. A point corresponds to one and
only one number on the ruler. This number
is called a coordinate . The following
postulate summarizes this concept.

Postulate 1-2-1

Ruler Postulate

The points on a line can be put
into a one-to-one correspondence
with the real numbers.

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The distance between any two points is the absolute value of the difference
of the coordinates. If the coordinates of points A and B are a and b, then the
distance between A and B is ⎜a - b⎟ or ⎜b - a⎟. The distance between A and B
̶̶
is also called the length of AB, or AB.

Congruent segments are segments that have
the same length.
In the diagram, PQ = RS, so you
_
_
can write PQ ≅ RS. This is read as “segment PQ
is congruent to segment RS.” Tick marks are
used in a figure to show congruent segments.